x^2-20x+14=0

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Solution for x^2-20x+14=0 equation:


Simplifying
x2 + -20x + 14 = 0

Reorder the terms:
14 + -20x + x2 = 0

Solving
14 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -20x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -20x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -20x + x2 = 0 + -14
-20x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-20x + x2 = -14

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -14 + 100

Reorder the terms:
100 + -20x + x2 = -14 + 100

Combine like terms: -14 + 100 = 86
100 + -20x + x2 = 86

Factor a perfect square on the left side:
(x + -10)(x + -10) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -10) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -10 = 9.273618495 Simplifying x + -10 = 9.273618495 Reorder the terms: -10 + x = 9.273618495 Solving -10 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.273618495 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.273618495 + 10 x = 9.273618495 + 10 Combine like terms: 9.273618495 + 10 = 19.273618495 x = 19.273618495 Simplifying x = 19.273618495

Subproblem 2

x + -10 = -9.273618495 Simplifying x + -10 = -9.273618495 Reorder the terms: -10 + x = -9.273618495 Solving -10 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.273618495 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.273618495 + 10 x = -9.273618495 + 10 Combine like terms: -9.273618495 + 10 = 0.726381505 x = 0.726381505 Simplifying x = 0.726381505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.273618495, 0.726381505}

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